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Diffusion Data for Silicate Minerals, Glasses, and Liquids

John B. Brady

1. INTRODUCTION

Diffusion is an integral part of many geologic processes and an increasing portion of the geologic literature is devoted to the measurement, estimation, and application of diffusion data. This compilation is intended to be a guide to recent experimentally- determined diffusion coefficients and, through the papers cited, to important older literature. To provide a context for the tables, a brief summary of the equations required for a phenomenological (macroscopic) description of diffusion follows. Although the equa - tions for well-constrained experiments are relatively straightforward, the application of the resulting diffusion coefficients to complex geologic problems may not be straightforward. The reader is urged to read one or more diffusion texts [e.g., 99, 121, 32, 147, 13.51 before attempting to use the data presented here.

2. FORCES AND FLUXES

Diffusion is the thermally-activated, relative movement (flux) of atoms or molecules that occurs in response to forces such as gradients in chemical potential or temperature. Diffusion is spontaneous and, therefore, must lead to a net decrease in free

J. B. Brady, Department of Geology, Smith College, North- ampton, MA 01063

Mineral Physics and Crystallography A Handbook of Physical Constants AGU Reference Shelf 2

Copyright 1995 by the American Geophysical Union.

energy. For example, the movement of An i moles of chemical component i from a region (II) of high chemical potential (/.Li”) to a region (I) of lower chemical potential (pi’) will cause the system Gibbs energy (G) to fall since

and using the definition of pi [ 139, p. 1281,

(2)

Thus, a chemical potential gradient provides a therm - odynamic force for atom movement.

On a macroscopic scale, linear equations appear to be adequate for relating each diffusive flux to the set of operative forces [137, p.451. The instantaneous, one-dimensional, isothermal diffusive flux JR (moles of i/m2s) of component i in a single-phase, n- component system with respect to reference frame R may be described by

(3)

where x (m) is distance and the n2 terms L: (moles of i/m.J.s) are “phenomenological diffusion coefficients” [36]. Because each component of the system may move in response to a gradient in the chemical potential of any other component, the complexity of describing diffusion in multicomponent systems rises

269

n i

i = 1

n

∑ d µ i = 0

BRADY 271

Table 1. Commonly-used solutions to equation (9)

Boundary Conditions Solution

Thin-film Solution Ci + CO for Ix]> 0 as t + 0 c, 3.00 for x = 0 as t + 0

} (y)=&exp[&) where cx=lL”(Ci -CO)dx (10)

Semi-infinite Pair Solution

1

Ci =CO for x>O at t=O C, =Cl for x<O at t=O 1

(E) = ierfc[--&=j (11)

Finite Pair Solution Ci =Cl for O<x<h at t=O Ci =CO for h<x<L at t=O

(ilC,/~x), =0 for x=0&L

Finite Sheet - Fixed Surface Composition

cases such as (12) and (13), the fractional extent of completion of homogenization by diffusion is propor- tional to a. These fi relations provide important tests that experimental data must pass if diffusion is asserted as the rate-controlling process. They also provide simple approximations to the limits of diffusion when applying measured diffusion coefficients to specific problems [ 1471.

4. DIFFUSION COEFFICIENTS

In general, one must assume that Di is a function of Ci. Therefore, equations (9)-( 13) may be used with confidence only if Ci does not change appreciably during the experiment. This is accomplished either (a) by using a measurement technique (typically involving radioactive tracers) that can detect very small changes in Ci, or (b) by using diffusional exchange of stable isotopes of the same element that leave the element concentration unchanged. Approach (a) yields a “tracer diffusion coefficient” for the element that is specific to the bulk composition studied. Approach (b) yields a “self-diffusion coeffi - cient” for the isotopically doped element that is also specific to the bulk chemical composition. Both approaches generally ignore the opposite or exchange flux that must occur in dominantly ionic phases such

as silicate minerals, glasses, and liquids. If Ci does change significantly in the experiment

and Di is a function of Ci, observed compositional profiles might not match the shape of those predicted by (9)-(13). In such cases the Di calculated with these equations will be at best a compositional “average” and equation (8) should be considered. Experiments in which composition does change significantly are often termed “interdiffusion” or “chemical diffusion” experiments. A commonly-used analytical solution to (8), for the same boundary conditions as for equation (1 1), was obtained by Matano [122] using the Boltzmann [8] substitution (x=x/& : 1

Equation (14) can be evaluated numerically or graphi - tally from a plot of (Ci - CO)/(Cl - CO) versus x, where the point x = 0 (the Matano interface) is selected such that

(15)

272 DIFFUSION DATA

0.0 1.0

(4 s 0.8 u

s u

3

; 0.6

x

9 3 0.4

-1.5 1.0 g 0.2

-2.0 0.0 0.2 0.4 0.6 0.8 1.0 0.2 0.4 0.6 0.8 1,

X2 x/L

Figure 1. Graphical solutions to equation (9). (A) The “thin film” solution of equation (10) is shown with a=1 for various values of fi (labels on lines). Plotting ln(Ci - CO) as a function of x2 at any time yields a straight line of slope -l/(4Dit). (B) The “finite pair” solution of equation (12) is shown for h/L=O.4 and various values of Dt/L2 (labels on curves). Plotting (Ci -CO)/(Cl - CO) as a function of x/L normalizes all cases to a single dimensionless graph. The initial boundary between the two phases is marked by a dashed vertical line.

[32, p.230-2341. For binary, cation exchange between ionic crystals, the Matano interface is the original boundary between the two crystals. Diffu- sion experiments that follow the Boltzmann-Matano approach have the advantage of determining Di as a function of Ci and the disadvantage of risking the complications of multicomponent diffusion, for which neither (8) nor (14) is correct.

Darken [35] and Hartley and Crank [83] showed that for electrically neutral species, the binary (AtiB) interdiffusion coefficients (D,,-, ) obtained in a Boltzmann-Matano type experiment and the tracer diffusion coefficients ( Da and D*,) for the interdiffus ing species are related by

D AB-, = (N,Di + NADIR)

where N A is the mole fraction and YA the molar activ- ity coefficient of component A. Darken developed his analysis in response to the experiments of Smigelskas and Kirkendall [ 1481, who studied the interdiffusion of Cu and Zn between Cu metal and Cu7&&~~ brass. Smigelskas and Kirkendall observed that MO wires (inert markers) placed at the boundary between the Cu and brass moved in the direction of the brass during their experiments, indicating that more Zn atoms than Cu atoms crossed the boundary. Darken’s analysis showed that in the presence of inert markers the

independent fluxes and, therefore, the “tracer” diffusion coefficients of Cu and Zn can be determined in addition to the interdiffusion coefficient DCuZnm,.

A similar analysis for binary cation interdiffusion (AZ w BZ where AZ represents Al”Z;’ and BZ represents BzbZ,“) in appreciably ionic materials such as silicate minerals yields [5, 112, 113, lo]:

I[

1 +

(17)

which requires vacancy diffusion if a#b. If a=b, then ( 17) simplifies to

D (Daz)( Diz )

AB-, = (NA,D;Z + NBZD;Z) Ii I +

(18)

[ 12 I]. This expression permits interdiffusion coefficients to be calculated from more-easily-measured tracer diffusion coefficients. For minerals that are not

BRADY 213

ideal solutions, the “thermodynamic factor” in brackets on the right side of (l6)-( 18) can significantly change the magnitude (and even the sign!) of interdiffusion coefficients from those expected for an idea1 solution [ 12, 251.

coefficients Dy to calculate multicomponent interdiffusion coefficient matrices, and its inverse offer the most hope for diffusion analysis of multicomponent problems [ 1 15, 19, 201. It should be noted in using equations ( I6)-( 19) that the tracer diffusivities themselves may be functions of bulk composition.

5. MULTICOMPONENT DIFFUSION 6. EXPERIMENTAL DESIGN

Rarely is diffusion in geologic materials binary. Multicomponent diffusion presents the possibility that diffusive fluxes of one component may occur in response to factors not included in (7)-( 1 S), such as gradients in the chemical potentials of other compo- nents, coupling of diffusing species, etc. In these cases, equation (6) or (3) must be used. The off- diagonal (i#j) diffusion coefficients, Dg or Li, are unknown for most materials and most‘workers are forced to assume (at significant peril!) that they are zero. Garnet is the one mineral for which off- diagonal diffusivities are available [ 19, 201 and they were found to be relatively small.

One approach used by many is to treat diffusion that is one-dimensional in real space as if it were one- dimensional in composition space. This approach was formalized by Cooper and Varshneya [28, 301 who discuss diffusion in ternary glasses and present criteria to be satisfied to obtain “effective binary diffusion coefficients” from multicomponent diffusion experiments. In general, diffusion coefficients obtained with this procedure are functions of both composition and direction in composition space. Another approach, developed by Cullinan [33] and Gupta and ,Cooper [75, 291, is to diagonalize the diffusion coefficient matrix for (6) through an eigenvector analysis. Although some simplification in data presentation is achieved in this way, a matrix of diffusion coefficients must be determined before the analysis can proceed.

Lasaga [105, see also 1611 has generalized the relationship (17) to multicomponent minerals. The full expression is quite long, but simplifies to

(19)

if the solid solution is thermodynamically ideal. In (19) zi is the charge on cation i, 411 = 1 if i=j, and 6il = 0 if i#j. This approach, usmg tracer diffusion

A few additional considerations should be mentioned regarding the collection and application of diffusion data.

l In anisotropic crystals, diffusion may be a function of crystallographic orientation and the diffusion coefficient becomes a second rank tensor. The form of this tensor is constrained by point group symmetry and the tensor can be diagonalized by a proper choice of coordinate system [ 13 I].

l Vacancies, dislocations, and other crystal defects may have profound effects on diffusion rates [e.g., 121, 1641. Therefore, it is essential that the mineral being studied is well-characterized. If the mineral, liquid, or glass contains a multivalent element like Fe, then an equilibrium oxygen fugacity should be controlled or measured because of its effect on the vacancy concentration.

l Diffusion in rocks or other polycrystalline materials may occur rapidly along grain boundaries, crystal interfaces, or surfaces and will not necessarily record intracrystalline diffusivities. Experiments involving grain-boundary diffusion [e.g., 102, 103, I 1, 47, 49, 95, 154, 13, 1581 are beyond the scope of this summary. If polycrystalline materials are used in experiments to measure “intrinsic” or “volume” diffusion coefficients, then the contributions of “extrinsic” grain-boundary diffusion must be shown to be negligible.

l Water can have a major effect on diffusion in many geologic materials, even in small quantities [e.g., 73, 150, 46, 167, 711. If water is present, water fugacities are an essential part of the experimental data set.

l Because many kinetic experiments cannot be “reversed,” every effort should be made to demonstrate that diffusion is the rate-controlling process. Important tests include the m relations noted in equations (lo)-( 13) and the “zero time experiment.” The @t test can be used if data are gathered at the same physical conditions for at least two times, preferably differing by a factor of four or more. The often-overlooked “zero time experiment,”

274 DIFFUSION DATA

which duplicates the sample preparation, heating to the temperature of the experiment, quenching (after “zero time” at temperature), and data analysis of the other diffusion experiments, commonly reveals sources of systematic errors.

These and other important features of diffusion experiments are described in Ryerson [141].

7. DATA TABLE

Due to space limitations, the data included in this compilation have been restricted to comparatively recent experimental measurements of diffusion coefficients for silicate minerals, glasses, and liquids. Many good, older data have been left out, but can be found by following the trail of references in the recent papers that are included. Older data may also be found by consulting the compilations of Freer [56, 571, Hofmann [86], Askill [2], and Harrop [81]. Some good data also exist for important non-silicate minerals such as apatite [ 157, 23, 451 and magnetite- titanomagnetite [65, 136,591, but the silicate minerals offered the clearest boundary for this paper.

Almost all of the data listed are for tracer or self- diffusion. Interdiffusion (chemical diffusion) experiments involving minerals are not numerous and interdiffusion data sets do not lend themselves to compact presentation. Interdiffusion data for silicate liquids and glasses are more abundant, but are not included [see 156, 3, 41. Neither are non-isothermal (Soret) diffusion data [see 1081. Diffusion data listed for silicate glasses and liquids have been further restricted to bulk compositions that may be classified as either basalt or rhyolite.

Because diffusion is thermally activated, coefficients for diffusion by a single mechanism at different temperatures may be described by an Arrhenius equation

D = D, exp (20)

and fit by a straight line on a graph of log D (m2/s) as a function of l/T (K-i) [147, Chap. 21. Log D, (m2/s) is the intercept of the line on the log D axis (l/T = 0). AHl(2.303.R) is the slope of the line where R is the gas constant (8.3143 J/mole.K) and

AH (J/mole) is the “activation energy.” D, and AH have significance in the atomic theory of diffusion [see 32, 1211 and may be related for groups of similar materials [162, 82, 1061.

Diffusion data are listed in terms of AH and log D, and their uncertainties. In many cases data were converted to the units &I, m2/s) and form (log D,) of this compilation. Logarithms are listed to 3 decimal places for accurate conversion, even though the original data may not warrant such precision. No attempt was made to reevaluate the data, the fit, or the uncertainties given (or omitted) in the original papers. Also listed are the conditions of the experiment as appropriate including the temperature range, pressure range, oxygen fugacity, and sample geometry. Extrapolation of the data using (20) to conditions outside of the experimental range is not advisable. However, for ease of comparison log D is listed for a uniform temperature of 800°C (1200°C for the glasses and liquids), even though this temperature may be outside of the experimental range. Use these tabulated log D numbers with caution.

Finally, a sample “closure temperature” (T,) has been calculated for the silicate mineral diffusion data. The closure temperature given is a solution of the Dodson [38] equation

for a sphere of radius a=O.l mm and a cooling rate (dT/dt) of 5 K/Ma. The example closure temperatures were included because of the importance of closure temperatures in the application of diffusion data to petrologic [107] and geochronologic [123, Chap. 51 problems. Note that other closure temperatures would be calculated for different crystal sizes, cooling rates, and boundary conditions.

Acknowledgments. This paper was improved by help- ful comments on earlier versions of the manuscript by D. J. Cherniak, R. A. Cooper, R. Freer, J. Ganguly, B. J. Giletti, S. J. Kozak, E. B. Watson, and an anonymous reviewer. N. Vondell provided considerable help with the library work.

Mineral, Glass, Orienta- Diffusing Temperature P 0, 4 log D, (or D) log D ‘IT,” Experiment/Comments Ref. or Liquid tion Component Range (“C) (MPa) (MPa) (kJ/mole) (m*/s) 8oo”c (“C)

m

E 4

Y WI

u Mineral, Glass, Orienta- Diffusing Temperature P 02 ma log D, (or D) log D ‘IT,” Experiment/Comments Ref. 7

or Liquid tion Component Range (“C) (MPa) (MPa) (kJ/mole) (m2/s) 800°C (“C)

[l@l ? 2

[loll

Mineral, Glass, Orienta- Diffusing Temperature P O2 4 log Do (or D) log D “T,” Experiment/Comments Ref. or Liquid tion Component Range (“C) (MPa) (MPa) (kJ/mole) (m*/s) 800°C (“C)

nepheline powder

biotite powder (see paper for camp.) phlogopite powder (see paper for camp.) phlogopite powder (Ann4) (see paper for camp.) biotite (An& powder (see paper for camp. reference) biotite powder

chlorite (sheridamte) (see paper) mucovite

powder

powder

muscovite (see powder paper for camp.)

‘80

180

4oAr

Sr

“wet” NO 650-800 100,20 uB/

2000 NO “wet”

650-800 100 UB/ “wet” NO

750-900 100 UBo “wet” NO

800 200 uB/ “wet” NO

c

r

I 104.6(+10.5) -12.229 -17.3 199 Exchange with CO*, spherical [27]

model, bulk analysis

-9.041

-7.854

-16.0

-16.4

233 Exchange with ‘*O-enriched [541 water, bulk analysis, cylindrical model, ion probe too

305 Exchange with 180-enriched [541 water, bulk analysis, cylin-

I ’ i

1’2”‘:’ 88

171.7 -5.21 -13.6

121.3 -7.98 -13.9

drical model, ion probe too 373 Degassing into water, bulk t621

analysis, cylindrical model, 671 (AV,zO m3/mole)

281 Degassing into water, bulk [771 analysis, cylindrical model (AV =1.4~10-~ m3/mole) Exchange with 41KC1 solu- F371

t

163 (+21) -8.114 -16.1

163 (f21) -11.699(f1.204) -19.6

172 (+25) -1l.OOO(f1.322) -19.4

239 (k8) -7.523 (f0.452) -19.1

268.2 (k7.1) -5.620 (f0.506) -18.7

D=lxlO-*’

t

t L

c

t

t

c

L

on, bulk analysis & ion

m

F 4

Y 4

ii

Mineral, Glass, Orienta- Diffusing Temperature P O2 4 log Do (or D) log D ‘IT,” Experiment/Comments Ref. u or Liquid tion Component Range (“C) (MPa) (MPa) (kllmole) (m2/s) 800°C (“C) ii

Sermanite (syn) lc-axis 1x0 02MgSi207) lkermanite (svn) I c-axis ‘80 (CazMgSizb;) 1 Sermanite (syn) ///c-axis / 45Ca UhMgSi207) Sermanite (syn) /c-axis 54Mn 02MgSi207) lkermanite (syn) /c-axis 59Fe 02MgSi207) &ermanite (syn) /c-axis 6oCo GbMgSbO,)

500-800 0.1 -12.2- -17.9 UB

1180 “wet” 0.1 w, 1

=I@‘4

1000-1300 0.1 co2

800-1300 0.1 (CO)/ co,:

1100-1300 0.1 N2

1100-1300 0.1 N2

1100-1300 0.1 N2

1100-1300 N2

I

i

robe, Rutherford backscatter,

m, sectioning, Ion probe, Rutherford backscatter,

I

I

I atmosphere, ion probe profile

Mineral, Glass, Orienta- Diffusing Temperature P 02 4 log D, (or D) log D “T,” Experiment/Comments Ref. or Liquid tion Component Range (“C) (MPa) (MPa) (kJ/mole) (m*/s) 800°C (“C)

Mineral, Glass, Orienta- Diffusing Temperature P O2 =a log Do (or D) log D “T,” Experiment/Comments Ref. or Liquid

g tion Component Range (“C) (MPa) (MPa) (kJ/mole) (m2/s) 800°C (“C)

2

olivine sintered 59Fe 1130 0.1 lo-to- n.d. n.d. log D59i+ = -10.143 + 0.2 [851 Wd%o-Faloo~ powder 10-12 , act + 2.705 [Fe/(Fe+Mg)]

olivine //c-axis Ni 1149-1234 evac. UB 193 (f10) -8.959 (f0.36) -18.4 / 404 Thin Ni film, microprobe G'61 (Fo93.7Fa6.3) tube profile, anisotropy found olivine (Fo,,Fas> //c-axis Fe-Mg 1125-1200 0.1 lo-l3 243 -5.759 -17.6 432 Microprobe profile, D varies [I41 fayalite powder (couple) interdiffusion w/direction, composition, fo2 olivine (Fa,,Te, )- //c-axis Fe-Mg 900-1100 evac. UB 208.5(+18.8) Do= 1.5(*0.3) Microprobe profile, D also ~1241 divine Fo91Fa9) (couple) interdiffusion tube +9.1 x [Mg/ x10-4) - 1.1x varies with direction and P

Wg+Fe)l [Mg/(Mg+Fe)] (AV =5,5~10-~m~/mole) a olivine(MgzSi04) //c-axis Co-Mg 1150-1300 0.1 air 196 -8.690 -18.2 ! 403 Microprobe profile, D’s [l-m - (Co2 SiO.+) (couple) interdiffusion 1300- 1400 526 2.288 -23.3 78 1 extrapolated to pure Fo forsterite - //c-axis Ni-Mg 1200-1450 0.1 air 414 to 444 -1.652 -21.8 702 Microprobe profile, other [1261 liebensbergite (couple) interdiffusion interdiffusion coefficients [128]

grossularite C&9 isotropic ‘80 1050 800 UB n.d. D=2.5~10-~~ Exchange with t80-enriched [581 Fe.1 Ah$hPd 850 200 nd. D=4.8xlO-2’ water, ion probe profiles almandine isotropic ‘80 8001000 100 UB 301 (+46) ,-8.222 (*0.740) -22.9 725 Exchange with ‘*O-enriched I311 (Al67SP2xAns b2) water, ion probe profiles ww isotropic 25Mg 750-900 200 uB/ 239 (*16) -8.009 -19.6 5 14 Thin 25Mg0 film, ion probe [341 E’m%GrdJrI ) MH profiles AlmsoPYPzo - isotropic Fe 1300-1480 2900- UBI 275.43 -7.194 -20.6 588 ! / Calculated from interdiffusion VOI Spess94Almg (couple) 4300 GrPC (rt36.49) experiments using model,

(AV,=5.6~10-~ m3/mole) AlmzoPYPzo - isotropic Mg 13001480 2900- UB/ 284.52 -6.959 -20.8 604 Calculated from interdiffusion WI Spessa4Alm6 (couple) 4300 GrPC (T37.55) experiments, (AV, =

5.6(f2.9)x10e6 m3/mole) AlmsoPYPzo - isotropic Mn 1300-1480 2900- UB/ 253.44 -7.292 -19.6 526 Calculated from interdiffusion m Spessa4Alm6 (couple) 4300 GrPC (k37.19) experiments, (AV, =

5.3(+3.0)x10-6 m3/mole) almandine isotropic 86Sr 800- 1000 100 UB 205 (+17) -12.000(&0.602) -22.0 616 Exchange with %r water [311 b’%SPd% pY2 ) solution, ion probe profiles almandine isotropic 145w 800-1000 100 UB 184 (+29) -12.523(*0.602) -21.5 ! 562 Exchange with 145Nd water 1311 b%SP2dnd’Y2) solution, ion probe profiles wope powder tslSm 1300-1500 3000 UB/ 140 -11.585 -18.4 321 Exchange with silicate melt, WI

GTPC autoradiography, “sphere” almandine isotropic 167 ET 800- 1000 100 UB 230 (f38) -10.301(?0.763) -21.5 605 Exchange with 167Er water [311 @l&Pd@Y2) solution, ion probe profiles AlmsoPYPzo - isotropic Fe-Mn 1300- 1480 4000 UBI 224.3 - 10.086 -21.0 57 1 Microprobe profiles, model [411 Spess94Alm6 (couple) interdiffusion GrPC (k20.5) fits of alm-rich composition

9 j!

Mineral, Glass, Orienta- or Liquid tion

Diffusing Temperature P O2 Component Range (“C) (MPa) (MPa)

=a (kJ/mole)

log D, (or D) log D “Tc” Experiment/Comments Ref. (m2/s) 1200°C (“C)

Zircon dissolution,

Mineral, Glass, Orienta- Diffusing Temperature P 0, aa log Do (or D) log D “Tc” Experiment/Comments Ref. or Liquid tion Component Range (“C) (MPa) (MPa) @J/mole) (m*/s) 1200°C (“C)

rhyolite glass and Ce 875-1100 0.1 air 490.4 2.72 (f0.99) -14.7 Thin film, serial sectioning by [91] (dehydrated) NM melt (f23.9) etching, counting surface rhyolite glass and Eu 700-1050 0.1 air 288.7 (k5.0) -3.11 (0.22) -13.3 Thin film, serial sectioning by [91] (dehydrated) NM melt etching, counting surface rhyolite (obsidian) melt 6% LREE 1000-1400 800 UB/ 251.5(*42.3) -4.638 (k1.436) -13.6 Monazite dissolution, [1381 Lake County, OR water GrPC microprobe profiles rhyolite (obsidian) melt 1% LREE 1000-1400 800 UB/ 510.9(+59.0) 3.362 (f0.629) -14.8 , Monazite dissolution, [1381 Lake County, OR water GrPC microprobe profiles rhyolite (obsidian) glass Hz0 400-850 0.1 Nz 103@5) -14.59 (f1.59) -18.2 Dehydration in Nz, FTIR [1661 Mono Craters profile, equilibrium model rhyolite (obsidian) glass H20 510-980 0.1 air 46.48 -10.90 (+0.56) -12.5 Dehydration in air, bulk 1931 New Mexico (fl 1.40) weight loss, low water rhyolite (obsidian) melt with 14CGz 800-1100 1000 UBI 75(?21) -7.187 -9.9 Thin film of Na2 14C03, B- 11551 Lake County, OR 8% water GrPC track profiles of cross section

basalt melt 6Li 1300-1400 0.1 air 115.5 -5.125 -9.2 Thin film of 6LiC1, ion probe [116] (alkali) profile of cross section basalt melt 0 1160-1360 0.1 IW to 215.9 -2.439 -10.1 Oxidation/reduction of bead, [1601 Goose Island co2 (f13.4) thermo-gravimetric balance basalt (alkali melt 0 1280-1400 400 UB/ 293(+29) -0.790 (k2.5 1) -11.2 Reduction by graphite, bulk ]401 olivine) BC GrPC Fe0 analysis by titration basalt (alkali melt 0 1280-1450 1200 UBI 360(+_25) 1.450 (t0.081) -11.3 Reduction by graphite, bulk ]401 olivine) BC GrPC Fe0 analysis by titration basalt (alkali melt 0 1350-1450 2000 uB/ 297 (+59) -0.770 (k1.87) -11.3 Reduction by graphite, bulk ]401 olivine) BC GrPC Fe0 analysis by titration basalt (tholeiite) melt 0 1300-1450 1200 uB/ 213 (k17) -3.010 (YkO.59) -10.6 Reduction by graphite, bulk [401 1921 Kilauea GrPC Fe0 analysis by titration basalt (FeTi) melt ‘80 1320-1500 0.1 Co2 251 (+29) -2.854 -11.8 Exchange with tsO-selected [I51 Galapagos ‘32 02 gas, bulk analysis of sphere “basalt” (Fe-free) melt Ar 1300-1450 looo- 113.2 (k7.5) -6.140 (kO.068) -10.2 [ Method not described r391’ (synthetic) 3000 basalt (“alkali”) melt 24Na 1300-1400 0.1 air 163 (+13) -4.02 (f0.46) -9.8 Thin film, serial sectioning by [116] Tenerife grinding, counting surface basalt (tholeiite) melt 45Ca 1260-1440 0.1 air 184.1 -4.272 -10.8 Thin film, B-track profiles of [891 1921 Kilauea cross-section on film “basalt” (Fe-free) melt 45Ca ilOO-14cKl 0.1 UB 106.3 -6.301 -10.1 Thin film of 45CaCl, B-track [152] ’ (synthetic) profiles of cross section “basalt” (Fe-free) melt 45Ca 1100-1400 1000 UB 141.0 -5.284 -10.3 Thin film of 45CaCl, B-track [152] 1 (synthetic) --I “basalt” (Fe-free) melt 45Ca 1100-1400 2000 UB 208.4 -3.211 -10.6 Thin film of 45CaCl, B-track t15211 (synthetic) profiles of cross section I

Mineral, Glass, Orienta- or Liquid tion

Diffusing Temperature P O2 Component Range (“C) (MPa) (MPa)

fia (kJ/mole)

log D, (or D) log D “Tc” Experiment/Comments Ref. (m2/s) 1200°C (“C)

T

basalt (“alkali”)

1921 Kilauea 1 basalt (“alkali”) 1

melt

melt

Tenerife basalt (“alkali”) melt Tenerife basalt (“alkali”) melt Tenerife basalt (tholeiite) melt 1921 Kilauea basalt (“alkali”) melt Tenerife basalt (tholeiite) melt

46Sc 1300-1400

54Mn

sSSr

1300-1400

59Fe

1 1300-1400

1300-1400

6OCo 1260-1440

6OCo 1300-1400

*%r 1260-1440

Tenerife basalt (tholeiite) melt 133& 1260-1440 1921 Kilauea basalt (“alkali”) melt 133& 1300-1400 Tenerife basalt (“alkali”) melt ‘Ts 1300-1400 Tenerife basalt (tholeiite) melt ‘=Eu, 1320-1440

Key to oxygen fugacity or atmosphere abbreviations in data table

0.1

0.1

0.1

0.1

0.1

0.1

0.1

0.1

0.1

0.1

0.1

air

air

air

air

air

air

air

air

air

air

air

ul3/ GrPC

CQ- GM - IW - h4H- N2 - NO -

Pure carbon dioxide atmosphere Graphite-methane buffer Iron-wustite buffer Magnetite-hematite buffer Pure nitrogen atmosphere Nickel-nickel oxide Pure oxygen atmosphere Quartz-fayalite-magnetite buffer

UB - Unbuffered oxygen fugacity UBlGrPC Unbuffered, but fo2 limited by the graphite-bearing piston-cylinder assembly UB/NO Unbuffered, but near nickel-nickel oxide due to the cold seal pressure vessel

hin film, serial sectionin

profiles of cross section,

284 DIFFUSION DATA

REFERENCES

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